How to efficiently merge geometry and get rid of internal shapes, etc?
You could try to merge vertices for a cleaner mesh by enabling the following options:


After that select a vertex RMB and move G displaced vertices over another vertex to merge them a circle appears around the target vertex confirm merge by LMB.

You could also add the reference image as a background image (only visible in orthographic mode). 

Method 1
Use extrusion modeling. Extrude single edges E, rotate them R scale them S and if required move single vertices. 
This is what @atomicbezierslinger describes.

Method 2
Extrude one single vertex E along the contour of the reference image and add faces later F.